The Sharma–Tasso–Olver–Burgers (STOB) equation is a nonlinear partial differential equation that appears in many branches of science, engineering and describes significant phenomena including wave propagation and fluid dynamics. The STOB equation characteristics and solutions for the nonlinear situation are thoroughly examined in this research work. The analytical techniques, namely the extended \((\frac{G'}{G^{2}})\) -expansion method, stability analysis, and sensitivity analysis, are used to determine the solitons solution of STOB equation. The study begins with an overview of the equation, highlighting its significance in modeling. The nonlinear nature of the equation leads to interesting dynamics and challenges in its analysis and solution. The research paper focuses on understanding the behavior of solutions and identifying the solution with the help of graphical interpretation. Numerous of the identified solutions are depicted in figures to provide a physical comprehension. Because it is critical, we use appropriate values of parameters to highlight the physical aspects of the supplied data using 3D, 2D, and contour charts. The proposed techniques are valuable and contribute to the field of nonlinear sciences. Various nonlinear evolutionary equations are employed to represent models of nonlinear physical phenomena
